Practicing with Maths Mela Class 5 Solutions Chapter 11 Grandmother’s Quilt Question Answer NCERT Solutions improves a student’s confidence in the subject.
Class 5 Maths Chapter 11 Grandmother’s Quilt Question Answer Solutions
Grandmother’s Quilt Class 5 Maths Solutions
Class 5 Maths Chapter 11 Solutions
(NCERT Pg 142)
Question 1.
Preetha and Adrit’s grandmother made a quilt cover using old clothes. Now she wants to decorate it with lace.
(i) Tick the lace option that would cover the entire border of the quilt.
(ii) She decides to use two different coloured laces. How much lace of each kind will be needed to cover the entire border?
Answer:
(i) From the picture of the quilt, we count that the quilt has 15 small rectangles along the horizontal side and 10 small rectangles along the vertical side.
So, the total length of the borders of the quilt will be 15+10+15+10 units.
i.e. 50 units.
Therefore, green lace would cover the entire border of the quilt.
(ii) Since, she needs a total of 50 units of lace. Then, one of the possible combinations of two different coloured laces to cover the entire border is
Red lace = 30 units
Blue lace = 20 units.
Let Us Do (NCERT Pg 142)
Question 2.
Find the perimeter of the following shapes. All sides of the following shapes are equal.
Answer:
(i) Given, shape has 5 sides, each having length 4 cm.
Then, the perimeter of the given shape
= 4+4+4+4+4 = 20 cm
(ii) Given, shape has 6 sides, each having length 5 cm.
Then, the perimeter of the given shape
= 5+5+5+5+5+5 = 30 cm
Question 3.
Draw two rectangles each having the following perimeters.
(i) 26 cm
(ii) 18 cm
Answer:
(i) Here, we can draw the following two rectangles having perimeter 26 cm.
(ii) Here, we can draw the following two rectangles having perimeter 18 cm.
(NCERT Pg 143)
Question 4.
Preetha and Adrit’s grandmother is making a rug with square patches. The picture below shows the rug. How many patches have they used to make this?
Answer:
From the figure, we count that there are 15 small square patches along the horizontal sides and there are 6 such horizontal strips of small square patches. Then, the total number of patches used
= 15 × 6 = 90
So, they have used 90 square patches to make the rug.
Question 5.
Preetha and Adrit are trying to cover their table with different shapes. Preetha covered it with triangles and circles. Adrit covered with squares and rectangles.
(i) They found that ________ and ________ shapes cover the top of the table without gaps and overlaps. ________ shape leaves gaps.
(ii) ________ triangles cover Table 1.
________ squares cover Table 3.
________ rectangles cover Table 4.
(iii) To find the area of the region, we usually fill it with shapes that tile (no gaps and overlaps), like squares, rectangles and triangles.
Do circles tile? Can we use them to cover a region?
The area of table 1 is ________ triangle units.
The area of table 3 is ________ square units.
The area of table 4 is ________ rectangle units.
Answer:
(i) Here, they found that triangle, square an rectangle shapes “over the top of the tabl without gaps and overlaps.
But, circle shape leaves gaps.
(ii) Here, 20 triangles cover table 1.
8 squares cover table 3.
12 rectangles cover table 4.
(iii) No, circle tiles leaves gaps. So, we can’t us them to cover a region.
Also,
The area of table 1 is 20 triangles units.
The area of table 3 is 8 squares units.
The area of table 4 is 12 rectangles units.
Question 6.
Now, try to cover the top of your table without gaps and overlaps with the following objects of same size.
(i) Notebooks
(ii) Lunch boxes
(iii) Pencil boxes
(iv) Maths textbooks
Which of the above objects covered the region completely?
Answer:
Do yourself.
Let Us Do (NCERT Pg 144)
Question 7.
Preetha is playing with tiles. She covers her desk with different shapes as shown below.
Look at the different tiles on her desk and answer how many of the following shapes will cover the desk.
(i) Green triangles ________
(ii) Red triangles ________
(iii) Blue squares ________
Answer:
From the figure, we count that the desk has 9 squares along the horizontal sides and there are 6 such horizontal strips of squares.
So, total number of square on her desk = 9 × 6 = 54.
(i) Here, we have
Since, each square contains 2 green triangle tiles and there are 54 squares.
So, there are total 54 × 2 i.e. 108 green triangles tiles which can cover her desk.
(ii) Here, we have
Since, 9 squares contains two red triangle tiles and there are 54 squares.
So, there are total (54 ÷9) × 2 i.e. 6 × 2 i.e. 12 red triangle tiles which can cover her desk.
(iii) Here, We have
Since, each square can admit one blue square tile and there are 54 squares.
So, there are total 54 blue square tiles which can cover her desk.
Comparing Shapes (NCERT Pg 144)
Question 8.
(i) Which of the above rectangles has the largest area? Trace these shapes on to a paper and cut them to find out the one that has the largest area. Do you see that the area of rectangle A is larger than that of B ? What above B and C ? Which shape has a larger area among A and C? How will you find out?
(ii) Let us put these rectangles on a square grid. Now, can you identify the rectangle that has the largest area?
Answer:
(i) Do yourself.
(ii) We know that area of 1 unit is 1 unit square.
So, area of rectangle A = 12 unit square, area of rectangle B = 8 unit square. and area of rectangle C = 10 unit square. Clearly, rectangle A has the largest area.
Let Us Do (NCERT Pg 145-147)
Question 9.
Compare the areas of the two gardens given below on the square grid. Share your observations.
Area of Garden A = ________ cm square
Area of Garden B = ________ cm square
Answer:
Since, from figure, it is clear that the garden A covers 10 squares of the square grid and garden B covers 12 squares of the square grid.
We know that 1 □ unit has area 1 square cm. So, area of garden A = 10 cm square and area of garden B = 12 cm square
Question 10.
Trace your palm on the square grid given below and find the approximate area of your palm. Compare the area of your palm with your friend’s palm. Who has a bigger palm?
Answer:
Do yourself.
Question 11 Collect leaves of different kinds. Put them on a square grid and find their area.
(i) Name the leaf with the largest area.
(ii) Name the leaf with the smallest area.
Answer:
Do yourself.
Question 12.
(i) The following mats are made of square patches of equal size. How many square patches will be required to cover each mat? Would both mats require an equal or different number of patches? Trace and cut out a small square of the size give below and find the area.
(a)
Area = ________
Perimeter = ________
(b)
Area = ________
Perimeter = ________
(ii) Trisha makes these two rectangles. She says, ” 1 increased the area of my rectangle and the perimeter increased.” Do you think this is always true?
(a)
(b)
Answer:
(i) (a) Here, we have
Clearly, 10 square patches will be required to cover the mat.
It has area of 10 unit squares because 1 □ unit has area 1 unit square and there are 10 such squares.
Also, the mat has 5 squares patches along horizontal side and 2 square patches along vertical side.
So, the perimeter of the mat is 5+2+5+2 i.e. 14 units.
(b) Here, we have
Clearly, 12 square patches will be required to cover mat.
Since, area of 1 □ unit is 1 unit square.
So, the area of the mat is 12 unit square. Clearly, the perimeter of the mat is 4+3+4+3 i.e. 14 units.
No, both the mats need different number of patches.
(ii) From figure (a), The area of rectangle = 6 unit square and the perimeter of rectangle
= 2+3+2+3
= 10 units
Also, from figure (b), The area of rectangle = 12 unit square and the perimeter of rectangle
= 3+4+3+4
= 14 units
It is very clear that when area of rectangle increases, the perimeter also increases.
So, Trisha’s statement is always true.
Let Us Explore (NCERT Pg 147-148)
Question 13.
Tick the shapes with the same area. Find the perimeters of these shapes. What do you notice? Discuss.
Answer:
We know that area of any shape is equal to the number of small squares on the square grid because 1 □ unit has area 1 square cm.
(i) Here, area of given shape = 1 × 12
= 12 square cm.
(ii) Here, area of given shape = 1 × 12
= 12 square cm
(iii) Here, area of given shape = 1 × 12
= 12 square cm
(iv) Here, area of given shape = 1 × 12
= 12 square cm
(v) Here, area of given shape = 1 × 8
= 8 square cm
(vi) Here, area of given shape = 1 × 12
= 12 square cm
Clearly, shapes (i), (ii), (iii), (iv) and (vi) have the same area.
Now, we know that perimeter of any shape is equal to the total length of the borders.
(i) Here, perimeter of given shape
= 6+2+6+2
= 16 cm
(ii) Here, perimeter of given shape
= 2+1+1+5+2+5+1+1
= 18 cm
(iii) Here, perimeter of given shape
= 3+4+3+4
= 14 cm
(iv) Here, perimeter of given shape
= 4+3+4+3
= 14 cm
(v) Here, perimeter of given shape
= 8+1+8+1
= 18 cm
(vi) Here, perimeter of given shape
= 12+1+12+1
= 26 cm
We notice that shapes having same area may have different perimeters.
Question 14.
Tick the shapes with the same perimeter. Find the areas of these shapes. What do you notice? Discuss.
Answer:
We know that perimeter of any shape is equal to the total length of the borders.
(i) Here, perimeter of given shape
= 3+3+1+1+2+2 = 12 cm
(ii) Here, perimeter of given shape
= 3+1+1+2+2+3 = 12 cm
(iii) Here, perimeter of given shape
= 2+1+1+1+1+1+1+1+1+1+1+1+1+2
= 16 cm
(iv) Here, perimeter of given shape
= 1+4+2+1+3+5 = 16 cm
(v) Here, perimeter of given shape
= 7+1+7+1 = 16 cm
Clearly, shapes (i) and (ii) have the same perimeter, that is 12 cm.
Also, shapes (iii), (iv) and (v) have the same perimeter, that is 16 cm.
Now, we know that area of 1 unit is 1 square cm. So, the area of any shape is equal to the number of small squares on the square grid covering that shape.
(i) Here, area of given shape = 7 square cm
(ii) Here, area of given shape = 7 square cm
(iii) Here, area of given shape = 7 square cm
(iv) Here, area of given shape = 7 square cm
(v) Here, area of given shape = 7 square cm
We notice that two shapes having same or different perimeters may have same area.
Let Us Do (NCERT Pg 149-150).
Question 15.
Draw different shapes having the same area as the given shape. Write the perimeter of each shape. What do you notice? Discuss.
Answer:
” We know that area of 1 unit is 1 square cm.
So, the area of given shape (i)
= 18 square cm
Now, we draw the different shapes having area 18 square cm as below
Then, area of rectangle = length × breadth
= 7 × 4 = 28 square cm
and the perimeter of rectangle
= 2 × length + 2 × breadth
= 2 × 7 + 2 × 4 = 14 + 8 = 22 cm
(iii) Do same as part (ii).
Length = 12 cm , Breadth = 4 cm,
Area = 48 square cm and perimeter = 32 cm.
(iv) Do same as part (i).
Length = 3 cm, Breadth = 3 cm,
Area = 9 square cm and perimeter = 12 cm.
(v) Do same as part (ii).
Length = 6 cm, Breadth = 5 cm,
Area = 30 square cm and perimeter = 22 cm.
Question 19.
Find the area and perimeter of the following objects. Use a scale or measuring tape to find the length and the breadth of each of the objects.
Answer:
Do yourself.
Question 20.
Find the area of a rectangular field, whose length is 42 m and breadth is 34 m.
Answer:
Given, length of the rectangular field = 42 m and breadth of the rectangular field = 34 m
Then, area of rectangular field
= length × breadth
= 42 × 34
= 1428 square m.
Question 21.
The area of a rectangular garden is 64 square m and.itsrength is 16 m. What is its breadth?
Answer:
Given, area of rectangular garden
= 64 square m
and length of the rectangular garden = 16 m
We know that area of a rectangle
= length × breadth
Then, 64 = 16 × breadth
⇒ Breadth = 64 ÷ 16 = 4
So, the breadth of the rectangular garden
= 4 m
Question 22.
Find the area of the following figure with the dimensions as marked in the figure.
Answer:
We first draw the given figure along with the clearly marked dimensions as below
Here, we have, length of the figure
= 32 cm
and breadth of the figure
= 6 cm+12 cm
= 18 cm
So, the area of the given rectangular figure
= length × breadth
= 32 × 18
= 576 square cm.